Intermediate Macroeconomics - Measurement (Continued) and Production

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```					 Intermediate Macroeconomics
Measurement (Continued) and Production

September 1, 2009

Intermediate Macroeconomics        September 1, 2009   1 / 68
Measuring Inﬂation

Inﬂation: Percent change in the price level.
What is the price level?

Two steps to calculate inﬂation:
(1) Measure a proxy for the price level called the price index
(2) Measure the growth rate of the price index

There are two famous price indexes:
GDP Deﬂator
Consumer Price Index (CPI)

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GDP Deﬂator

The GDP deﬂator is backed out from real GDP and nominal GDP

Find the Nominal GDP measure (GDP N )
Find the Real GDP measure (GDP R )

N
GDPt
¯
Pt =          R
GDPt

¯     ¯
Pt+1 −Pt
Inﬂation =          ¯
Pt

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GDP Deﬂator
What is the inﬂation rate (measured by the deﬂator) in this
example?

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Consumer Price Index

The CPI gives the average price of a ﬁxed basket of consumer
goods
It is calculated by the Bureau of Labor Statistics (BLS)

The BLS visits and calls stores, collecting prices

For any good, they calculate a change in price

The price changes are weighted by purchasing habits
Consumer Expenditure Survey (CES)

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Measuring Saving and Wealth

Saving : (Current Income) minus (Current “used up” Goods)
Is Investment used up?
Are Consumer Durables used up?

National Saving (S): National Income minus “Used Up” Goods
≈GDPt                Ct +Gt

Private Saving (S pvt ): Disposable Income minus Consumption
≈(GDPt −Taxest )           Ct

Government Saving (S gov ): Gov Income minus Gov Spending
≈Taxest       Gt
National Saving = Private Saving + Government Saving
“Saving”

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Uses for Private Saving

St = GDPt − Ct − Gt

St = (Ct + It + Gt + NXt ) − Ct − Gt

St = It + NXt
where NX ≈ Current Account (CA)

Stpvt = It + CAt + (−Stgov )
Deﬁcit
Since St =    Stpvt   + Stgov

Intermediate Macroeconomics   September 1, 2009   7 / 68
Relating Saving and Wealth

Back to stock and ﬂow

Saving is the ﬂow into the stock of national wealth(W)

St + St+1 + St+2 + ... + ST = WT

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Measuring Interest Rates

Interest: A fee charged by a lender to a borrower .
Interest Rate: The fee divided by the amount borrowed
FEE
i=   AMOUNT BORROWED

Real versus Nominal Interest Rates
Nominal interest rate (i): The interest rate at current prices
Real interest rate(r): The interest rate at constant prices

Fisher Equation:
i = r+ inﬂation rate

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Interest Rates

Intermediate Macroeconomics   September 1, 2009   10 / 68
The Production Function

Inputs ⇒ Production Function ⇒ Output

Y = F (INPUTS)

Economists call inputs “factors of production”
Labor (N): Time spent working
Capital (K): Amount of goods used to make other goods

Y = F (K , N)

What other types of inputs are we missing?

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Desirable Properties of the Production Function

Economists want a function with the following properties:

All inputs ⇑ causes Output ⇑

Inputs work together to make output

Holding one input ﬁxed, will make another input not work as
well

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The Cobb-Douglass Production Function

Y = K α N 1−α
F (K ,N)

Doubling (or tripling, or..) both N and K ⇒ Y to double (or
triple,..)

F(2N,2K) = 2Y
F(3N,3K) = 3Y
For any z ≥ 0, F(zN,zK) = zY
This is called Constant Returns to Scale

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The Cobb-Douglas Production Function

Y = K α N 1−α
F (K ,N)

αK = α: Capital’s Share of Output
αN = 1 − α: Labor’s Share of Output

Y = K αK N αN

Economists have measured αK = 0.3 and αN = 0.7

Y = K 0.3 N 0.7

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The Cobb-Douglas Production Function

Overall productivity (A) makes all inputs work better:

Y = AF(K,N)

A is usually called total factor productivity (TFP).

Intermediate Macroeconomics              September 1, 2009   15 / 68
The Cobb-Douglas Production Function
Y = F(K,N) is a three-dimensional function:

Output

Capital

Labor

Very complicated to understand what’s going on!
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The Cobb-Douglas Production Function

So we look at altering one input at a time, holding the other ﬁxed

¯
If labor is ﬁxed: N
¯
If capital is ﬁxed: K

“Fixed” means they are treated as “parameters” (i.e. speciﬁc
numbers, not variables)

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The Cobb-Douglas Production Function

Holding Labor Fixed

Y

N               K

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The Cobb-Douglas Production Function
Holding Labor Fixed

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The Marginal Product of Capital

Holding Labor Fixed:

¯
Y = AF (K , N)

What happens to output when we adjust capital?

Notation:
∆ means change
∆K : change in capital
∆Y : change in output

What happens to ∆Y when we change capital (i.e ∆K = 0)?
∆Y
Marginal Product of Capital (MPK) =        ∆K

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The Marginal Product of Capital

Intermediate Macroeconomics   September 1, 2009   21 / 68
The Marginal Product of Labor

Holding Capital Fixed:

¯
Y = AF (K , N)

What happens to output when we adjust labor?

What happens to ∆Y when ∆N = 0?
∆Y
Marginal Product of Labor (MPN) =           ∆N

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The Marginal Product of Labor
Holding Capital Fixed

Intermediate Macroeconomics   September 1, 2009   23 / 68
Changes in Productivity

TFP (or A) is considered is considered an exogenous “parameter”
in most models.
∆A: Productivity shock
Often called supply shock

Intermediate Macroeconomics         September 1, 2009   24 / 68
Supply (Productivity) Shock

Intermediate Macroeconomics   September 1, 2009   25 / 68

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